Abstract

Studying the spectroscopic properties of nuclei in terms of their nucleonic degrees of freedom is one of the most challenging tasks in nuclear structure physics. In principle, the nuclear Shell Model (SM) allows to solve exactly the nuclear eigenvalue problem. Its actual implementation, however, presents several problems.
One has first to turn the eigenvalue problem in the full space into an equivalent one formulated in a restricted model space. In order to achieve this step, it is necessary to find a reliable method for deriving an effective Hamiltonian, acting into the model space, from the bare nucleon nucleon interaction.
Another difficulty deals with the dimensions of the SM Hamiltonian matrix. In fact, they grow very rapidly with the number of active nucleons, even in a small model space. It is therefore necessary to search for efficient algorithms which allow to diagonalize large Hamiltonian matrices.
The first part of this work has consisted in upgrading an iterative diagonalization algorithm developed few years ago [1], so as to allow large scale nuclear shell model calculations in the uncoupled m-scheme. This new version can generate a large number of extremal eigenstates for each angular momentum and, therefore, is able to provide a complete description of the low energy properties of complex nuclei.
The method has been applied to heavy Xenon isotopes. We have investigated first the convergence properties of the iterative procedure, which has allowed to asses the limits of the method [2]. Within these limits, it has been possible to give a complete description of their properties by computing the spectra and E2 and M1 transition strengths [3]. The analysis of the results has allowed to determine the collectivity of the states as well as their proton-neutron symmetry and multiphonon nature.
Due to the limited dimensions of the space, shell model calculations are not able to provide a complete picture of collective modes, especially of the high energy resonances. In order to describe correctly these modes, we have reformulated an equation of motion method [4], which generates iteratively a basis of multiphonon states, built of TDA phonons, and uses such a basis to solve the eigenvalue problem.
The method, which is free of approximations, has been applied to the closed shell Oxygen 16 and to neutron rich oxygen isotopes, using a realistic effective Hamiltonian in a space which includes up to three-phonon states. We have studied the effect of these complex states on the giant dipole resonance, and, for neutron rich nuclei, on the so-called pygmy resonance.
The method and some preliminary results have been presented in recent international conferences. A complete description will be submitted soon for publication on an international journal.
[1.] F. Andreozzi, N. Lo Iudice, and A. Porrino, J. Phys. : Nucl. Part. Phys. 29, 2319 (2003).
[2.] D. Bianco, F. Andreozzi, N. Lo Iudice, A. Porrino, and F. Knapp, J. Phys. G 38, 025103(2011).
[3.] D. Bianco, F. Andreozzi, N. Lo Iudice, A. Porrino, and F. Knapp, Phys. Rev. C 84, 024310 (2011).
[4.] F. Andreozzi, F. Knapp, N. Lo Iudice, A. Porrino, and J. Kvasil, Phys. Rev. C 75, 044312 (2007).